12.7 Multiphase flows
399
boundary layer. Nieuwstadt et al. (1991) discuss results of a number of authors who used codes based on finite-volume methods. At the global scale,
finite-volume methods are used but a spectral method specifically designed
for the surface of a sphere is more common. This method uses spherical harmonics as the basis functions.
In choosing a time-advancement method, one must take into account the
need for accuracy but it is also important to note that wave phenomena play
a significant role in both meteorology and oceanography. The large weather
systems that are familiar from weather maps and satellite photographs may
be regarded as very large scale traveling waves. The numerical method must
not amplify or dissipate them. For this reason, it is quite common t o use the
leapfrog method in these fields. This method is second-order accurate and
neutrally stable for waves. Unfortunately, it is also unconditionally unstable
(it amplifies exponentially decaying solutions) so it must be stabilized by
restarting it approximately every ten time steps. There are a number of ways
of doing this; one of the simplest is to use a different method for one time
step.
12.7 Multiphase flows
Engineering applications often involve multiphase flows; examples are solid
particles carried by gas or liquid flows (fluidized beds, dusty gases, and slurries), gas bubbles in liquid (bubbly fluids and boilers) or liquid droplets in
gas (sprays), etc. A further complication is that multiphase flows often occur
in combustion systems. In many combustors, liquid fuel or powdered coal is
injected as a spray. In others, coal is burned in a fluidized bed.
The methods described in the previous section may be applied to some
types of two-phase flows, especially those in which both phases are fluids.
In these cases, the interface between the two fluids is treated explicitly as
described above. Some of the methods were specifically designed for this
type of flow. However, the computational cost associated with the treatment
of interfaces limits these methods to flows in which the interfacial area is
relatively small.
There are several other approaches to computing two-phase flows. The
carrier or continuous phase fluid is always treated by an Eulerian approach,
but the dispersed phase may be handled by either a Lagrangian or an Eulerian
met hod.
The Lagrangian approach is often used when the mass loading of the dispersed phase is not very large and the particles of the dispersed phase are
small; dusty gases and some fuel sprays are examples of flows to which this
method might be applied. In this approach, the dispersed phase is represented
by a finite number of particles or drops whose motion is computed in a Lagrangian manner. The number of particles whose motion is tracked is usually
399
boundary layer. Nieuwstadt et al. (1991) discuss results of a number of authors who used codes based on finite-volume methods. At the global scale,
finite-volume methods are used but a spectral method specifically designed
for the surface of a sphere is more common. This method uses spherical harmonics as the basis functions.
In choosing a time-advancement method, one must take into account the
need for accuracy but it is also important to note that wave phenomena play
a significant role in both meteorology and oceanography. The large weather
systems that are familiar from weather maps and satellite photographs may
be regarded as very large scale traveling waves. The numerical method must
not amplify or dissipate them. For this reason, it is quite common t o use the
leapfrog method in these fields. This method is second-order accurate and
neutrally stable for waves. Unfortunately, it is also unconditionally unstable
(it amplifies exponentially decaying solutions) so it must be stabilized by
restarting it approximately every ten time steps. There are a number of ways
of doing this; one of the simplest is to use a different method for one time
step.
12.7 Multiphase flows
Engineering applications often involve multiphase flows; examples are solid
particles carried by gas or liquid flows (fluidized beds, dusty gases, and slurries), gas bubbles in liquid (bubbly fluids and boilers) or liquid droplets in
gas (sprays), etc. A further complication is that multiphase flows often occur
in combustion systems. In many combustors, liquid fuel or powdered coal is
injected as a spray. In others, coal is burned in a fluidized bed.
The methods described in the previous section may be applied to some
types of two-phase flows, especially those in which both phases are fluids.
In these cases, the interface between the two fluids is treated explicitly as
described above. Some of the methods were specifically designed for this
type of flow. However, the computational cost associated with the treatment
of interfaces limits these methods to flows in which the interfacial area is
relatively small.
There are several other approaches to computing two-phase flows. The
carrier or continuous phase fluid is always treated by an Eulerian approach,
but the dispersed phase may be handled by either a Lagrangian or an Eulerian
met hod.
The Lagrangian approach is often used when the mass loading of the dispersed phase is not very large and the particles of the dispersed phase are
small; dusty gases and some fuel sprays are examples of flows to which this
method might be applied. In this approach, the dispersed phase is represented
by a finite number of particles or drops whose motion is computed in a Lagrangian manner. The number of particles whose motion is tracked is usually